Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems.opinion dynamics, consensus/dissent, bounded confidence, nonlinear dynamical systems.

Truth and Cognitive Division of Labour: First Steps Towards a Computer Aided Social Epistemology

The paper analyzes the chances for the truth to be found and broadly accepted under conditions of cognitive division of labour combined with a social exchange process. Cognitive division of labour means, that only some individuals are active truth seekers, possibly with different capacities. The social exchange process consists in an exchange of opinions between all individuals, whether truth seekers or not. We de- velop a model which is investigated by both, mathematical tools and computer simulations. As an analytical result the Funnel theorem states that under rather weak conditions on the social process a consensus on the truth will be reached if all individuals posses an arbitrarily small inclination for truth seeking. The Leading the pack theorem states that under certain conditions even a single truth seeker may lead all individuals to the truth. Systematic simulations analyze how close and how fast groups can get to the truth depending on the frequency of truth seekers, their capacities as truth seekers, the position of the truth (more to the extreme or more in the centre of an opinion space), and the willingness to take into account the opinions of others when exchanging and updating opinions. A tricky movie visualizes simulations results in a parameter space of higher dimensions.Opinion Dynamics, Consensus/dissent, Bounded Confidence, Truth, Social Epistemology

A new method to suppress the bias in polarized intensity

Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. To develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that closely follows the signal from the source. We propose a new method to suppress the bias by estimating the polarisation angle of the source signal in a noisy environment with help of a modified median filter. We then determine the polarised intensity, including the noise, by projection of the observed values of Stokes U and Q onto the direction of this polarisation angle. We show that our new method represents the true signal very well. If the noise distribution in the maps of U and Q is Gaussian, then in the corrected map of polarised intensity it is also Gaussian. Smoothing to larger Gaussian beamsizes, to improve the signal-to-noise ratio, can be done directly with our method in the map of the polarised intensity. Our method also works in case of non-Gaussian noise distributions. The maps of the corrected polarised intensities and polarisation angles are reliable even in regions with weak signals and provide integrated flux densities and degrees of polarisation without the cumulative effect of the bias, which especially affects faint sources. Features at low intensity levels like 'depolarisation canals' are smoother than in the maps using the previous methods, which has broader implications, for example on the interpretation of interstellar turbulence.Comment: accepted for publication in Astronomy & Astrophysic

The NOD3 software package: A graphical user interface-supported reduction package for single-dish radio continuum and polarisation observations

The venerable NOD2 data reduction software package for single-dish radio continuum observations, developed for use at the 100-m Effelsberg radio telescope, has been successfully applied over many decades. Modern computing facilities call for a new design. We aim to develop an interactive software tool with a graphical user interface (GUI) for the reduction of single-dish radio continuum maps. Special effort is given on the reduction of distortions along the scanning direction (scanning effects) by combining maps scanned in orthogonal directions or dual- or multiple-horn observations that need to be processed in a restoration procedure. The package should also process polarisation data and offer the possibility to include special tasks written by the individual user. Based on the ideas of the NOD2 package we developed NOD3, which includes all necessary tasks from the raw maps to the final maps in total intensity and linear polarisation. Furthermore, plot routines and several methods for map analysis are available. The NOD3 package is written in Python which allows to extend the package by additional tasks. The required data format for the input maps is FITS. NOD3 is a sophisticated tool to process and analyse maps from single-dish observations that are affected by 'scanning effects' due to clouds, receiver instabilities, or radio-frequency interference (RFI). The 'basket-weaving' tool combines orthogonally scanned maps to a final map that is almost free of scanning effects. The new restoration tool for dual-beam observations reduces the noise by a factor of about two compared to the NOD2 version. Combining single-dish with interferometer data in the map plane ensures the full recovery of the total flux density.Comment: 8 pages, 10 figures, Accepted for publication in A&

Enhancement of magnetic fields arising from galactic encounters

Galactic encounters are usually marked by a substantial increase of synchrotron emission of the interacting galaxies compared to the typical emission from similar isolated galaxies. This is believed to be associated with an increase of the star formation rate and the associated turbulent magnetic fields. The regular magnetic field is usually believed to decrease. We consider a simple, however rather realistic, mean-field galactic dynamo model where the effects of small-scale generation are represented by random injections of magnetic field from star forming regions. We represent an encounter by the introduction of large-scale streaming velocities and by an increase in small-scale magnetic field injections. The latter describes the effect of an increase of the star formation rate caused by the encounter. We demonstrate that large-scale streaming, with associated deviations in the rotation curve, can result in an enhancement of the anisotropic turbulent (ordered) magnetic field strength, mainly along the azimuthal direction, leading to a significant temporary increase of the total magnetic energy during the encounter; the representation of an increase in star formation rate has an additional strong effect. In contrast to expectations, the large-scale (regular) magnetic field structure is not significantly destroyed by the encounter. It may be somewhat weakened for a relatively short period, and its direction after the encounter may be reversed. The encounter causes enhanced total and polarized emission without increase of the regular magnetic field strength. The increase of synchrotron emission caused by the large-scale streaming can be comparable to the effect of the increase of the star formation rate, depending on the choice of parameters.The effects of the encounter on the total magnetic field energy last only slightly longer than the duration of the encounter (ca. 1 Gyr).Comment: 9 pages, 11 figures minor changes in response to referee's comments+linguistic/stylistic change

Dyadic facial affective indicators of severity of symptomatic burden in patients with panic disorder

Background: Based on the results of research on facial affective behaviour in different psychological disorders, as well as on available findings on the specific behaviour of patients with panic disorder in interaction with their therapists, hypotheses about dyadic facial affective behaviour and its correlation with symptomatic burden of female panic patients are formulated. Sampling and Methods: The facial affective behaviour of 20 patients with panic disorder and their therapists, coded with EMFACS, in the first treatment session is analyzed regarding interactive enmeshment, and for a subgroup of 15 dyads these data are correlated with those on symptomatic burden before treatment. Results: A high degree of interactive enmeshment between patient and therapist correlates positively with the severity of symptomatic burden. All dyadic enmeshment indicators show highly significant positive correlations with body-related symptoms, but not with more general variables like global severity index of the SCL-90R or general anxiety (STAI). Conclusions: These results are discussed against the background of the specific psychodynamic of panic patients and show that, on the one hand, therapists practise an interactive abstinence, but on the other hand, they tend to be pulled into a specific interactive enmeshment by patients with greater symptomatic burden. Limitations of the study arise from the small sample and the lack of a comparison-group, therefore the question if the results are disorder-specific or more general cannot be answered

The formation of regular interarm magnetic fields in spiral galaxies

Observations of regular magnetic fields in several nearby galaxies reveal magnetic arms situated between the material arms. The nature of these magnetic arms is a topic of active debate. Previously we found a hint that taking into account the effects of injections of small-scale magnetic fields generated, e.g., by turbulent dynamo action, into the large-scale galactic dynamo can result in magnetic arm formation. We now investigate the joint roles of an arm/interarm turbulent diffusivity contrast and injections of small-scale magnetic field on the formation of large-scale magnetic field ("magnetic arms") in the interarm region. We use the relatively simple "no-$z$" model for the galactic dynamo. This involves projection on to the galactic equatorial plane of the azimuthal and radial magnetic field components; the field component orthogonal to the galactic plane is estimated from the solenoidality condition. We find that addition of diffusivity gradients to the effect of magnetic field injections makes the magnetic arms much more pronounced. In particular, the regular magnetic field component becomes larger in the interarm space compared to that within the material arms.The joint action of the turbulent diffusivity contrast and small-scale magnetic field injections (with the possible participation of other effects previously suggested) appears to be a plausible explanation for the phenomenon of magnetic arms.Comment: 9 pages, 9 figure

Testing the cosmological evolution of magnetic fields in galaxies with the SKA

We investigate the cosmological evolution of large- and small-scale magnetic fields in galaxies at high redshifts. Results from simulations of hierarchical structure formation cosmology provide a tool to develop an evolutionary model of regular magnetic fields coupled to galaxy formation and evolution. Turbulence in protogalactic halos generated by thermal virialization can drive an efficient turbulent dynamo. The mean-field dynamo theory is used to derive the timescales of amplification and ordering of regular magnetic fields in disk and dwarf galaxies. For future observations with the SKA, we predict an anticorrelation at fixed redshift between galaxy size and the ratio between ordering scale and galaxy size. Undisturbed dwarf galaxies should host fully coherent fields at z<1, spiral galaxies at z<0.5.Comment: 2 pages, contribution to the proceedings of the IAU Symposium 259 "Cosmic Magnetic Fields: from Planets, to Stars and Galaxies", Puerto Santiago, Tenerife, Spain, November 3-7, 2008 (in press